An American and European put both have strike price $25, the same underlying asset and the same time to expiry. Consider a three-step binomial model. The underlying asset price is, in crr notation, S = $24 , u = 1.15 and d = 1/u . The return over each time step is R = 1.05 .

(a) Construct a three-step binomial pricing tree for the European put and find the premium then constuct a three-step binomial pricing tree for the American put and find the premium.

(b) If the European put is a down-and-out barrier option with barrier at the asset price $20. Construct a three-step binomial pricing tree for this barrier European put and find the premium.

(c) If the American put is a down-and-out barrier option with barrier at the asset price $20. Construct a three-step binomial pricing tree for this barrier American put and find the premium.